System and method for three-dimensional complete tooth modeling

ABSTRACT

A system and method for modeling of complete tooth, including root and crown, of a patient to facilitate orthodontic treatment are provided, wherein a generic tooth modeling is combined with a tooth crown modeling for a patient to yield a complete tooth modeling. In accordance with an exemplary embodiment, a generic tooth three-dimensional model for a particular tooth is morphed with a three-dimensional model of a patient&#39;s crown for the corresponding tooth to yield a complete three-dimensional model for that tooth. Such modeling techniques can be conducted with one or more computer-based systems, such as systems configured for storing patient data and generic tooth data, morphing such data and/or facilitating additional orthodontic treatment applications, through the use of one or more algorithms. Further adjustment of the complete tooth model for the tooth can also be provided through additional patient information, such as X-ray imaging, to address variations in root shape between a generic root and an actual root shape for a patient.

TECHNICAL FIELD

The present invention relates, generally, to dental and/or orthodontictreatment, and in particular to a system and method forthree-dimensional modeling of a complete tooth and/or teeth, includingroot and crown, of a patient to facilitate dental and/or orthodontictreatment.

BACKGROUND OF THE INVENTION

The ability to provide an accurate and complete modeling of teeth is animportant element in the growing field of computational orthodontics andother computer aided dental treatment systems. Current techniques forimpression-based computational orthodontics are limited to crownmodeling of the patient's tooth, such as the capturing of crown and gumshape information, but do not capture or utilize corresponding rootinformation. As a result, such impression techniques do not provide forthe root component within the present tooth model, and fail to accountfor root movement and/or interaction within the gums, thus limiting theability of the complete tooth model in facilitating orthodontictreatment. Such failure to account for root movement can also result inroot collision that hinders the orthodontic treatment process.

A complete tooth model, comprising both root and crown components foreach tooth, could be extremely beneficial for providing optimumdiagnostics, treatment planning and analysis, such as for example, instage planning and simulation, collision detection, finite elementanalysis, biometrics and mass property calculations to name a few.

SUMMARY OF THE INVENTION

In accordance with various aspects of the present invention, a systemand method for three-dimensional modeling of a complete tooth and/orteeth, including both root and crown, of a patient to facilitate dentaland/or orthodontic treatment are provided, wherein a generic tooth modelcomprising generic root and crown components is combined with acrown-only model of one or more actual teeth of a patient to yield acomplete tooth model comprising both root and crown components. Inaccordance with an exemplary embodiment, a generic tooththree-dimensional model for a particular tooth is generated and thenautomatically morphed with a three-dimensional model of a patient'sactual crown for the corresponding tooth to yield a completethree-dimensional model for that tooth. Such a process can be suitablyapplied for any and all of the various teeth within a patient, such asmolars, bicuspids, canines or any other teeth within a patient. Variousexemplary embodiments can comprise methods and systems for automatedgeneration of morphing landmarks, model segmentation, root and crownstitching and/or three-dimensional root model adjustment. Such modelingtechniques can be conducted with one or more computer-based systems,such as systems configured for storing actual patient data and generictooth data, morphing generic tooth data to such patient's data and/orfacilitating additional orthodontic treatment applications, through theuse of one or more algorithms.

In accordance with an exemplary embodiment, further adjustment of thecomplete tooth model for the tooth can be provided through additionalpatient information regarding the actual root and/or crown, such asX-ray imaging and the like, to address variations in root shape betweena morphed generic root and an actual root shape for a patient so as toyield a root shape on the tooth model which more closely approximatesthe actual root shape of the actual tooth.

BRIEF DESCRIPTION OF THE DRAWINGS

The exemplary embodiments of the present invention will be described inconnection with the appended drawing figures in which like numeralsdenote like elements, and wherein:

FIGS. 1A-1C illustrate diagrams of an exemplary system and method formodeling of tooth root and crown of a patient in accordance with anexemplary embodiment of the present invention;

FIG. 2 illustrates a flow diagram of an exemplary method of toothmodeling in accordance with an exemplary embodiment of the presentinvention;

FIGS. 3A-3C illustrate a flow diagram and graphical representations ofan exemplary method of modeling a generic teeth template in accordancewith an exemplary embodiment of the present invention;

FIGS. 4A-4D illustrate a flow diagram and graphical representations ofan exemplary method of automatic landmark generation for tooth crown inaccordance with an exemplary embodiment of the present invention;

FIGS. 5A and 5B illustrate a flow diagram and a graphical representationfor an exemplary method for root and crown mesh generation in accordancewith an exemplary embodiment of the present invention;

FIGS. 6A-6F illustrate a flow diagram and graphical representations andcurves for an exemplary method for automatic stitching of the crown withthe root in accordance with an exemplary embodiment of the presentinvention;

FIGS. 7A and 7B illustrate exemplary three-dimensional tooth models forstitching of the crown and root with and without smoothing processes,respectively, in accordance with exemplary embodiments of the presentinvention;

FIGS. 8A-8C illustrate a flow diagram and a graphical representationsand curves for an exemplary method for morphing control by rootlandmarks in accordance with an exemplary embodiment of the presentinvention;

FIGS. 9A and 9B illustrate exemplary three-dimensional complete toothmodels and an exemplary user interface for interactive root adjustmentin accordance with an exemplary embodiment of the present invention;

FIGS. 10A-10C illustrate exemplary diagrams for root widgets inaccordance with an exemplary embodiment of the present invention; and

FIGS. 11A-11F illustrate an exemplary flow diagram and graphicalrepresentations for automatic complete tooth model adjustment usingX-ray data in accordance with an exemplary embodiment of the presentinvention.

DETAILED DESCRIPTION

The present invention may be described herein in terms of variouscomponents and processing steps. It should be appreciated that suchcomponents and steps may be realized by any number of hardware andsoftware components configured to perform the specified functions. Forexample, the present invention may employ various electronic controldevices, visual display devices, input terminals and the like, which maycarry out a variety of functions under the control of one or morecontrol systems, microprocessors or other control devices. In addition,the present invention may be practiced in any number of orthodontic ordental contexts and the exemplary embodiments relating to a system andmethod for modeling of complete tooth of a patient as described hereinare merely a few of the exemplary applications for the invention. Forexample, the principles, features and methods discussed may be appliedto any orthodontic or dental treatment application or process.

It should be noted that for illustrative purposes, the various exemplarymethods and systems may be described in connection with a single toothof a patient; however, it should be understood that such exemplarymethods and systems can be suitably implemented on more than one toothand/or all teeth within a patient, such as molars, bicuspids, canines orany other teeth within a patient. For example, the exemplary methods andsystems can be suitably implemented by performing a particular process,operation or step on one or more teeth before proceeding to a subsequentprocess, operation or step, or by performing all or essentially allprocesses, operations or steps on a particular tooth before proceedingto another tooth, or any combination thereof.

In accordance with various aspects of the present invention, a systemand method for modeling of complete tooth, including root and crown, ofa patient to facilitate orthodontic treatment are provided, wherein ageneric tooth model is combined with a corresponding tooth crown modelfor a patient to yield a complete tooth modeling. For example, withreference to FIGS. 1A-1C, in accordance with an exemplary embodiment, asystem for modeling tooth root and crown 100 comprises a generic tooththree-dimensional model 102 for an exemplary tooth configured forcombination with a three-dimensional model 104 of a patient's crown forthe corresponding tooth to yield a complete three-dimensional model 106for that tooth. Generic tooth model 102 is configured to provide ageneric three-dimensional modeling of both root and crown for aparticular tooth of a patient, such as generic tooth model 101. In apreferred embodiment, generic tooth model 102 will be of the same typeof tooth (e.g. molar, canine, bicuspid and the like) as the actual toothit is intended to model. Moreover, in other exemplary embodiments,generic tooth model 102 can be the same numbered tooth as the actualpatient tooth, using conventional tooth numbering and identificationsystems. Patient tooth crown model 104 can be suitably generated byvarious techniques for tooth crown modeling to generate athree-dimensional patient tooth crown 103, such as those disclosed inU.S. Pat. No. 6,685,469, assigned to Align Technology, Inc. (the “'469Patent”), or such modeling processes known and provided under the brandsINVISALIGN® and CLINCHECK® that are available under Align Technology,Inc. of Santa Clara, Calif. The creation of complete tooth model 106 canbe suitably realized by an automated morphing of generic tooth modeling102 and patient tooth crown model 104, such as by a computer algorithmwithin a tooth model system 112, for the creation of a three-dimensionalcomplete tooth 105, with such processes being applied to any or allteeth within the patient.

The exemplary modeling methods can be conducted with one or morecomputer-based systems, such as a system 110 configured for storingpatient data and generic tooth data, a tooth modeling system 112configured for generating generic tooth model 102 and patient toothcrown model 104 and for morphing data and information from model 102 andmodel 104 to generate complete tooth model 106, and a system 114configured for facilitating any other conventional orthodontic treatmentapplications, such as methods or processes for tracking teeth movementand position, evaluating gingival effects, or any other orthodontictreatment process from pre-treatment to final stages, or any stages inbetween. Systems 110, 112 and/or 114 can comprise one or moremicroprocessors, memory systems and/or input/output devices forprocessing modeling data and information. To facilitate modeling of rootand crown of a patient, tooth modeling system 112 can comprise one ormore software algorithms configured for generating complete tooth model106 and/or performing other functions set forth herein.

In accordance with an exemplary embodiment, further adjustment of thecomplete tooth model for the tooth can be provided through detailedadjustment modeling 108. For example, additional patient informationregarding the actual root of a patient, such as X-ray imaginginformation provided from a radiograph 107, can be suitably utilized bytooth modeling system 112 to address variations in root shape between ageneric root and an actual root shape for a patient so as to yield aroot shape on complete tooth model 105 which more closely approximatesthe actual root shape of the actual tooth. Such additional actual rootinformation can comprise various formats and generated in variousmanners. For example, X-ray imaging information can comprise, forexample, panoramic, periapical, bitewing, cephalometric or other likeinformation, for facilitating further detailed modeling.

With reference to FIG. 2, a flow diagram illustrates an exemplarycomputer-implemented method 200 for modeling of tooth root and crown ofa patient comprises a method 202 for generating a generic tooth model, amethod 204 for generating a patient tooth crown model, and a method 206for generating a complete tooth model through combination of a morphedgeneric root model with a corresponding patient tooth crown model.Method 200 can be suitably utilized to provide both generic tooth modelsand crown tooth models for each tooth of a patient, thus enabling acomplete tooth model for any and/or all teeth of a patient to beobtained for facilitating orthodontic treatment.

Generic tooth modeling method 202 is configured to provide a referencefor construction for complete tooth modeling, such as the generation ofa generic tooth 101 comprising both root and crown for a particulartooth. In accordance with an exemplary embodiment, generic toothmodeling 202 comprises the generation of a generic tooth model template(208), auto-segmenting of a generic crown from the generic root withinthe generic tooth model (210), and automatic creation of landmarks onthe generic crown (212).

Generating of a generic tooth model template (208) is configured tofacilitate the creation of landmarks on the generic tooth model to allowfor morphing with the patient tooth crown model. For example, in orderto generate adequately distributed landmarks and to accurately segmentthe crown from the tooth, the setup of generic teeth data is provided togenerate a generic tooth template. With reference to a flow diagramillustrated in FIG. 3A, in accordance with an exemplary embodiment, aprocess 300 for generating of a generic tooth model template cancomprise the acquisition of data from a physical tooth model (302), thedecimating of tooth model data (304), the setting up a generic toothcoordinate system (306), the constructing of a generic tooth digitalmodel (308), the identifying of gingival curves (310) and the creatingof template file(s) associated with the generic teeth (312). Theacquisition of data from a physical tooth model data (302) can comprisethe scanning of a standard typodont or any other three-dimensionalmodels for demonstrating alignment of teeth within a patient to generatethree-dimensional digital template data.

Such typodont or models that are used for scanning can comprise both anexemplary root and crown for a single tooth or multiple teeth of apatient. In addition, such typodont or generic models can be suitablyprovided based on different configurations of teeth, e.g., differentsizes, shapes, and/or caps, different types of teeth such as molars,bicuspids or canines, and/or different occlusal patterns orcharacteristics, e.g., overbite, underbite, skewed or other likemisalignment patterns. In accordance with an exemplary embodiment, theroot shape, configuration or component for such typodont models cancomprise the same generic root configuration for all types of teeth. Inaccordance with other exemplary embodiments, the root component for suchtypodont models can comprise a typical generic root configuration for atype of tooth, e.g., a typical root shape or configuration for molars,bicuspids and/or canines can be provided, based on one type for allpatients, or based on whether the patient is a child or adult, male orfemale, or any other demographic or characteristic that might beassociated with different types of teeth. Moreover, in accordance withother exemplary embodiments, the root component for such typodont modelscan comprise a typical generic root shape or configuration for aspecific actual tooth, e.g., a specific root shape for a particularcanine tooth can be used with the specific crown shape for thatparticular canine tooth to generate the typodont model, again based onone configuration for that particular tooth all patients, or based ondifferent configurations for that specific tooth depending on whetherthe patient is a child or adult, male or female, or any otherdemographic or characteristic that might be associated with differenttypes of teeth.

As such, generic models for any type of teeth characteristic or type canbe provided and suitably utilized, allowing great flexibility inspecializing for different teeth structures, occlusal patterns andcharacteristics of a patient. In addition, any conventional devices,systems and/or methods for the scanning of physical models, such astypodonts, to generate data can be utilized, such as known techniquesfor generating initial digital data sets (IDDS), including that setforth in U.S. Pat. No. 6,217,325, assigned to Align Technology, Inc.

To reduce the amount of data and/or filter out any undesirable dataafter such acquisition of data from the typodont or generic tooth model,the decimating of data (304) can be conducted, such as the removal ordeletion of data or otherwise the finding of optimal data values throughthe elimination at a constant fraction of the scanning data; however,the decimating of data (304) can also be suitably omitted or otherwisereplaced by any filtering or data enhancement techniques.

Whether or not the scanned data is decimated, the developing of ageneric tooth coordinate system (306) can be undertaken, such as tosetup or develop a generic tooth coordinate system as illustrated inFIG. 3B. The coordinate system can be set-up automatically and/oradjusted manually, using any conventional or later developed techniquesfor setting up coordinate systems of an object. Upon generation of acoordinate system for a generic tooth, the constructing of a digitalgeneric tooth model (308) comprising root and crown can be conducted foran individual tooth and/or two or more teeth. Such constructing ofdigital tooth models can comprise any methodology or process forconverting scanned data into a digital representation. Such methodologyor processes can include, for example, those disclosed in U.S. Pat. No.5,975,893, entitled “Method and System for Incrementally Moving Teeth”assigned to Align Technology, Inc. For example, with reference to anoverall method for producing the incremental position adjustmentappliances for subsequent use by a patient to reposition the patient'steeth as set forth in U.S. Pat. No. 5,975,893, as a first step, adigital data set representing an initial tooth arrangement is obtained,referred to as the IDDS. Such an IDDS may be obtained in a variety ofways. For example, the patient's teeth may be scanned or imaged usingwell known technology, such as X-rays, three-dimensional x-rays,computer-aided tomographic images or data sets, magnetic resonanceimages, etc. Methods for digitizing such conventional images to producedata sets are well known and described in the patent and medicalliterature. By way of example, one approach is to first obtain a plastercast of the patient's teeth by well known techniques, such as thosedescribed in Graber, Orthodontics: Principle and Practice, SecondEdition, Saunders, Philadelphia, 1969, pp. 401-415. After the toothcasting is obtained, it can be digitally scanned using a conventionallaser scanner or other range acquisition system to produce the IDDS. Thedata set produced by the range acquisition system may, of course, beconverted to other formats to be compatible with the software which isused for manipulating images within the data set. General techniques forproducing plaster casts of teeth and generating digital models usinglaser scanning techniques are described, for example, in U.S. Pat. No.5,605,459.

After constructing of the generic tooth digital model (308), theidentifying of the gingival curve (310) can be conducted to identify thegum lines and/or root association. Such identification can comprise anyconventional computational orthodontics methodology or process foridentification of gingival curves, now known or hereinafter derived. Forexample, the methodologies and processes for identification of gingivalcurves can include those disclosed in U.S. Pat. No. 7,040,896, entitled“Systems and Methods for Removing Gingiva From Computer Tooth Models”,and assigned to Align Technology, Inc. (the “'896 Patent”) and U.S. Pat.No. 6,514,074, entitled “Digitally Modeling the Deformation ofGingival”, and assigned to Align Technology, Inc. (the “'074 Patent”),and the various patents disclosed in the '896 and '074 Patents. In the'896 Patent, for example, such a process for identification of gingivalcurves can comprise a computer-implemented method separates a tooth froman adjacent structure, such as a gingiva, by defining a cutting surface,and applying the cutting surface between the tooth and the structure toseparate the tooth in a single cut. In the '074 Patent, for example,such a process for identification of gingival curves can comprise havinga computer obtain a digital model of a patient's dentition, including adental model representing the patient's teeth at a set of initialpositions and a gingival model representing gum tissue surrounding theteeth, wherein the computer then derives from the digital model anexpected deformation of the gum tissue as the teeth move from theinitial positions to another set of positions.

Having constructed the digital generic tooth model (308) and identifiedthe gingival curve (310), one or more generic tooth template files canbe created (312), such as the exemplary generic teeth templateillustrated in FIG. 3C comprising substantially a complete set of teethof a patient. Such generic teeth templates can then be suitably utilizedto allow for segmenting of crowns and landmark distribution on thegeneric teeth. In addition, such generic teeth templates can be suitablyutilized for one or more treatments, and/or replaced or updated withother generic teeth templates as desired. Moreover, such generic teethtemplates can be suitably created and/or stored for later use, and canbe configured for various differences in patients, such as forchildren-based templates and adult-based templates, with the ability tohave a plurality of templates that are specially created for thedifferent types of teeth and related characteristics, sizes, shapes, andocclusal patterns or other features.

With reference again to FIG. 2, after generic teeth templates have beengenerated, automated segmenting of a generic crown from the generic rootwithin the generic tooth template (210) can be conducted to prepare thegeneric tooth template for landmark creation. In this process, the crownportion of the generic tooth template is suitably parceled out and/oridentified to allow mapping during landmark processes.

For the generic tooth, the crown and root geometry can be extracted fromthe generic tooth model. After such extraction or segmentation, thecrown/root mesh can be suitably generated. For example, with referenceto FIGS. 5A and 5B, a process 500 for automated crown/root meshgeneration can comprise the construction of the 3D spline curve (502),wherein control points on the transition area between the tooth crownand root are utilized, such as that illustrated in FIG. 5B. Next, theprojection of the 3D spline curve on the tooth mesh model (504) can beconducted. A calculation of the intersection between the projected curveand the edges of triangle faces of the mesh (506) can then be made tofacilitate the construction of new triangles (508). In this process, thethree original vertices of the intersected triangle and the twointersection points can be utilized to construct three new triangles,such as by use of the Delaunay triangulation's max-min angle criterion.After such construction, the re-triangulation of the old intersectedtriangle and replacing that old triangle with the three newly generatedtriangles (510) can be conducted. Upon re-triangulation and replacement,the generation of new crown/root mesh model (512) can be realized byremoving all the faces below/above the projected curve, resulting in asegmented generic tooth crown/root. Processes 502, 504, 506, 508, 510and 510 can be provided through any known conventional techniques forproviding such functions, or hereinafter devised.

Once the crown of the generic tooth template has been segmented,automated creation of landmarks on the generic crown (212) can beperformed prior to morphing with the patient tooth crown model. Inaccordance with an exemplary embodiment, with reference to FIGS. 4A-4D,landmarks can be created on a crown sphere (402) and then the landmarkscan be projected onto a crown surface (404). For example, a tooth crowncan be suitably mapped to a sphere by central projection, as illustratedin FIG. 4B. The landmarks can be created on the sphere throughappropriate distribution on each of a plurality of cross-sections, e.g.,cross-sections through the Z-axis, perpendicular to the X-Y plane. Forexample, as illustrated in a representative cross-section shown in FIG.4C, a plurality of landmarks 406 can be created on a sphere 410 withappropriate distribution. The number of landmarks 406 can be determinedthrough parameters such as the number of planes to be considered whilesweeping through the Z-axis, and the number of points selected for eachplane. Once landmarks 406 are created on the crown sphere (402),landmarks can be suitably projected onto the crown surface, such aslandmarks 408 projected onto the crown surface in FIG. 4C, and landmarks408 illustrated in FIG. 4D that comprise landmarks 408 projected onto ascan of a patient's crown 420 and a generic tooth crown 430 comprising aroot and crown template. Such an automated generation can be facilitatedby one or more algorithms within a tooth modeling system, and can besuitably computed for each patient tooth and generic tooth. Theplurality of landmarks 408 on generic tooth crown 430 and thecorresponding landmarks 408 on the patient tooth crown 420 will be usedfor calculating the morphing function.

With reference again to FIG. 2, method 204 for generating a patienttooth crown model can comprise the generation of an initial patienttooth model without root (214), i.e., generation of a crown tooth model,automated detection of the crown geometry (216) and the automatedcreation of landmarks on the patient crown tooth model (218). Generatingthe crown tooth model (214) can be suitably realized by various knownmethods and techniques, including various conventional scanningtechniques used in computational orthodontics for creating IDDS and thelike.

For example, such an IDDS can be derived from the above methods and/oras set forth in U.S. Pat. No. 6,217,325, also assigned to AlignTechnology, Inc. In an exemplary embodiment, to obtain an IDDS, thepatient's teeth may be scanned or imaged using well known technology,such as X-rays, three-dimensional X-rays, computer-aided tomographicimages or data sets, magnetic resonance images, etc. Methods fordigitizing such conventional images to produce data sets useful in thepresent invention are well known and described in the patent and medicalliterature. Usually, however, an IDDS procurement will rely on firstobtaining a plaster cast of the patient's teeth by well knowntechniques, such as those described in Graber, Orthodontics: Principleand Practice, Second Edition, Saunders, Philadelphia, 1969, pp. 401-415.After the tooth casting is obtained, it can be digitally scanned using aconventional laser scanner or other range acquisition system to producethe IDDS. The data set produced by the range acquisition system may, ofcourse, be converted to other formats to be compatible with the softwarewhich is used for manipulating images within the data set, as describedin more detail in U.S. Pat. No. 6,217,325. General techniques forproducing plaster casts of teeth and generating digital models usinglaser scanning techniques are described, for example, in U.S. Pat. No.5,605,459.

In addition, there are a variety of range acquisition systems, generallycategorized by whether the process of acquisition requires contact withthe three dimensional object. A contact-type range acquisition systemutilizes a probe, having multiple degrees of translational and/orrotational freedom. By recording the physical displacement of the probeas it is drawn across the sample surface, a computer-readablerepresentation of the sample object is made. A non-contact-type rangeacquisition device can be either a reflective-type or transmissive-typesystem. There are a variety of reflective systems in use. Some of thesereflective systems utilize non-optical incident energy sources such asmicrowave radar or sonar. Others utilize optical energy. Thosenon-contact-type systems working by reflected optical energy furthercontain special instrumentation configured to permit certain measuringtechniques to be performed (e.g., imaging radar, triangulation andinterferometry). For example, a preferred range acquisition system is anoptical, reflective, non-contact-type scanner. Non-contact-type scannersare preferred because they are inherently nondestructive (i.e., do notdamage the sample object), are generally characterized by a highercapture resolution and scan a sample in a relatively short period oftime. One such scanner is the Cyberware Model 15 manufactured byCyberware, Inc., Monterey, Calif. Moreover, either non-contact-type orcontact-type scanners may also include a color camera, that whensynchronized with the scanning capabilities, provides a means forcapturing, in digital format, a color representation of the sampleobject.

Upon generating the crown tooth model, automatic detection of the crowngeometry (216) is conducted to prepare the tooth model for creation oflandmarks. For the patient tooth model, the crown geometry can besegmented from the entire tooth using any conventional process forsegmentation of crowns from teeth. Upon detecting the crown geometry,the automated creation of landmarks on the patient crown tooth model canbe provided, such as the techniques (212) utilized on the generic crownmodel, e.g., those illustrated by FIGS. 4A-4D.

Upon generation of the generic tooth model (202) and the crown toothmodel (204), generation of the complete tooth model (206) can beconducted through combination/morphing of the generic tooth model withthe corresponding patient tooth crown model. In accordance with anexemplary embodiment, a method for generating a complete tooth model(206) can comprise calculating the morphing function (220), calculatingthe patient root (222), stitching the patient crown to the patient root(224), smoothing the root-crown transition area (226) and conductinginteractive adjustment of the patient root if necessary (228). Suchprocesses can be completely conducted for individual teeth beforeproceeding to any other teeth, conducted concurrently, or any othercombination thereof.

For calculating of the morphing function 220, in accordance with anexemplary embodiment, a thin-plate spline can be utilized to calculatethe morphing function by the created landmarks. Use of such a thin-platespline can minimize the deformation energy effects, e.g., minimize thedegree or extent of bent in the resulting surface between createdlandmarks. In addition, the Euclidian points distance or surfaceshortest distance between landmarks is utilized for calculation of themorphing function through:

${\int{\int_{R^{2}}\left( \frac{\partial^{2}f}{\partial^{2}x^{2}} \right)^{2}}} + {2\left( \frac{\partial^{2}f}{{\partial x}{\partial y}} \right)^{2}} + {\left( \frac{\partial^{2}f}{\partial^{2}y^{2}} \right)^{2}\ {x}{y}}$

Once the morphing function is calculated (220), the patient rootgeometry can be suitably calculated (222), such as by applying themorphing function on the generic root model.

In some cases, the patient crown is quite different from the generictooth crown. When this occurs, using only the crown landmarks formorphing control may prove insufficient, as the root shape and directionmay be difficult to control. In accordance with another exemplaryembodiment, improved morphing control can be realized by creatinglandmarks on the root central axis. For example, with reference to FIG.8A, in the first morphing process, the crown landmarks can be utilizedto calculate the initial morphing function, which is used to obtain amorphed central axis (802), such as illustrated in FIG. 8B. Next, thecentral axis of the generic tooth can be suitably moved to be tangent tothe morphed central axis (804), such as illustrated in FIG. 8C. Aftermovement of the central axis of the generic tooth, the repositionedcentral axis of the generic tooth can be suitably scaled such that itslength is equal to the morphed central axis in the Z-direction. As aresult, both the crown landmarks and the root landmarks and can be thenutilized to calculate the final morphing function.

After calculation of the patient root (222) through morphing of thegeneric tooth root, the patient crown is stitched to the patient root togenerate the complete 3D tooth model (224).

To facilitate stitching, the crown mesh and the root mesh are suitablymerged. For example, with reference to FIG. 6A, the stitching processcomprises the projecting of the 3D loops onto the X-Y plane (602), suchas illustrated in FIG. 6B. Since the projected loops are homogeneous toa circle, the loop vertices can be re-sorted by angle to construct amerged loop (604), such as illustrated in FIG. 6C. Next,re-triangulation of the crown mesh and the root mesh can be conducted(606). Upon re-triangulation, the crown mesh and root mesh can be merged(608) to obtain a topologically correct complete tooth mesh.

After stitching (224), the crown-root transition area of the completetooth model can be suitably smoothed (226) to improve the model. Forexample, with reference to FIG. 7A, after the stitching process, thetransition area may not be very smooth. However, through use of asuitably smoothing algorithm, the stitching can be suitably smoothed,such as illustrated in FIG. 7B. The smoothing algorithm operates as afilter to essentially remove “noise” from the stitched points within thetransition area. For example, the algorithm can identify or target afirst point, then observe neighboring points to suitably tweak orotherwise adjust the first point to smooth out the stitching. Thealgorithm can be suitably conducted for each tooth within the patient.Such an algorithm can also comprise various formats and structures forproviding the smoothing function.

After smoothing of the crown-root transition (226), interactive rootadjustment (228) can be provided. With reference to FIG. 9A, thecomplete 3D root model can be adjusted by length or rotation on demand.For example, all the length of all roots, adjust all roots X-rotation,or the adjustment of one root. Such adjustment can be suitably carriedout through a user interface, such as that illustrated in FIG. 9B,and/or automatically by the modeling system, to achieve a desiredcriteria. As a result, the complete tooth model is generated for use infacilitating treatment.

As briefly discussed, in some instances, after generation of thecomplete tooth model, the generated root shape may vary from the actualroot shape due to the individual features of the patient. With referenceagain to FIG. 1 in accordance with an exemplary embodiment, furtheradjustment of the complete tooth model for the tooth can be providedthrough detailed adjustment modeling 108. For example, additionalpatient root information regarding features or characteristics of theactual root, such as can be obtained from X-ray imaging informationprovided from a radiograph 107, can be suitably utilized by toothmodeling system 112 to address the variations in root shape between ageneric root and an actual root shape for a patient so as to yield aroot shape on complete tooth model 105 which more closely approximatesthe actual root shape of the actual teeth.

Such additional actual root information can comprise various formats andgenerated in various manners. For example, X-ray imaging information cancomprise, for example, panoramic, periapical, bitewing, cephalometric orother like information, for facilitating further detailed modeling. Inaddition, since such X-ray imaging information generally comprises a 2Dimage, the X-ray information can be considered approximately as a 2Dprojection from the facial side to the lingual side. As a result, thefurther detailed adjustment is based on one-view information, whereinthe algorithm suitably makes the modeled root shape coincide with theactual root shape based on such one-view information.

For example, with reference to FIG. 11A, a method for detailedadjustment modeling can begin with the projection of the complete toothmodel, e.g., one derived after morphing/combination (206) of method 200,on a single plane, whose normal is from a tooth's facial side to atooth's lingual side (1102). Next, the contour of the complete tooth canbe calculated (1104) and defined, such as the tooth contour Aillustrated in FIG. 11B. The corresponding patient tooth can be suitablyidentified from the X-ray information, such as from panoramic X-rayimage (1106), and the contour of the corresponding tooth can also becalculated from that X-ray image (1108) and defined, such as the toothcontour B illustrated in FIG. 11C. Any conventional methodology orprocess for calculation and/or determination of contours can be readilyutilized for determining the contours of tooth A and tooth B. Next, thescaling in size between the complete tooth contour (e.g., contour A),and the corresponding patient tooth contour (e.g., contour B) can bedetermined (1110), and then the corresponding patient tooth contour canbe scaled to have to have the same crown contour as the complete toothcontour (1112). In accordance with another exemplary embodiment, insteadof scaling complete tooth contour (1112), thin-plate spline basedmorphing function can be used to deform the corresponding patient toothcrown contour to the complete tooth crown contour. For example, themorphing function can be calculated by the landmarks on thecorresponding patient tooth crown contour and complete tooth crowncontour. Landmarks can then be generated (1114) on the root domain ofthe complete tooth contour (e.g., contour A), and the correspondingtooth contour (e.g., contour B), such as illustrated with reference toFIGS. 11D and 11E. Based on the generated landmarks, and the calculationof the morphing function, the complete tooth contour can be suitablymorphed onto a projection plane (1116), such as illustrated in FIG. 11F.Such morphing can be conducted through similar processes as disclosed inmorphing/combining process 206, e.g., by calculating a morphing function(220) and applying the morphing function of the root portion (222).Accordingly, a complete tooth model for any one and/or all teeth of apatient, suitably adjusted through an accounting of a patient'sindividual and/or specialized features and characteristics, can berealized.

The complete tooth models comprising root portions can be used tofurther facilitate planning and treatment processes. Additional stepscan also be introduced to further improve the planning and treatmentprocesses. As an example, to create an enhanced clinical meaningfulmovement, a root widget can be created for use in manipulating thetooth. In particular, with reference to FIGS. 10A-10C, a clinicallymeaningful root widget can be created at the center of resistance of atooth. In this embodiment, the center of rotation of the tooth isconsidered to be at approximately ⅓ of the tooth length from the rootapex along the vertical axis of the tooth. The axis of the tooth can beestablished by any conventional methodology or process for establishingaxis and/or coordinate systems within teeth.

Another treatment process that can be implemented is to monitor thespeed of root movement for a tooth to determine which teeth are movingmore aggressively. Use of the root geometry can be readily used tofacilitate this calculation. For example, the movement speed from astage n to a stage n+1 is defined by the formula:

m = ∫_(s)dist(x, y, z) s

where (x,y,z) is the point on the root surface and dist(x,y,z) is themoving distance of this point from stage n to a stage n+1. Thedist(x,y,z) can be computed by the length of the trajectory of the point(x,y,z) from its position a stage n to the position at stage n+1. As aresult, treatment adjustments to teeth based on their speed of rootmovement can be conducted to further enhance the treatment process.

The present invention has been described above with reference to variousexemplary embodiments. However, those skilled in the art will recognizethat changes and modifications may be made to the exemplary embodimentswithout departing from the scope of the present invention. For example,the various operational steps, as well as the components for carryingout the operational steps, may be implemented in alternate waysdepending upon the particular application or in consideration of anynumber of cost functions associated with the operation of the system,e.g., various of the component and methodologies and/or steps may bedeleted, modified, or combined with other components, methodologiesand/or steps. Moreover, it is understood that various of the methods andsteps disclosed herein, such as generating of IDDS, construction of 3Dspline curves, identifying or gingival curves or other processes canalso comprise any other conventional techniques, or any later developedtechniques, for facilitating such methods and steps. These and otherfunctions, methods, changes or modifications are intended to be includedwithin the scope of the present invention, as set forth in the followingclaims.

1. A computer-implemented method for modeling of a complete tooth of apatient to facilitate dental and/or orthodontic treatment, saidcomputer-implemented method for modeling comprising: generating at leastone patient digital tooth model comprising a crown component; generatingat least one generic digital tooth model corresponding to said at leastone patient digital tooth model, said at least one generic digital toothmodel comprising both root and crown components; and morphing said atleast one patient digital tooth model with said at least one genericdigital tooth model to provide a complete digital tooth model of thepatient.
 2. The computer-implemented method according to claim 1,wherein generating said at least one generic digital tooth modelcomprises: providing a generic tooth model template comprising a genericroot and a generic crown; segmenting of said generic crown from saidgeneric root within said generic tooth model template; and automaticallycreating landmarks on said generic crown.
 3. The computer-implementedmethod according to claim 2, wherein providing the generic tooth modeltemplate comprises: acquiring data representing a physical tooth model;setting up a generic tooth coordinate system; constructing of a generictooth digital model; and creating of template file(s) associated withsaid generic tooth.
 4. The computer-implemented method according toclaim 3, wherein generating a generic tooth model template furthercomprises identifying of a gingival curve associated with said generictooth model prior to creating of template file(s) associated with saidgeneric tooth.
 5. The computer-implemented method according to claim 3,wherein acquiring data representing a physical tooth model comprisesscanning of the physical tooth model to generate three-dimensional data.6. The computer-implemented method according to claim 5, whereinscanning of the physical tooth model comprises scanning a generic rootshape for a specific tooth type and a generic crown shape for saidspecific tooth type to generate said three-dimensional data.
 7. Thecomputer-implemented method according to claim 3, further comprisingdecimating of said acquired data.
 8. The computer-implemented methodaccording to claim 2, wherein segmenting of said generic crown from saidgeneric root within said generic tooth model template comprisesparceling out a generic crown component to facilitate mapping of saidgeneric crown component during the creating of landmarks.
 9. Thecomputer-implemented method according to claim 2, wherein creatinglandmarks on said generic crown comprises creating landmarks on a crownsphere for said generic tooth model.
 10. The computer-implemented methodaccording to claim 9, wherein creating landmarks on a crown sphere forsaid generic tooth model comprises mapping said landmarks on the crownsphere appropriately distributed on cross-sections.
 11. Thecomputer-implemented method according to claim 2, wherein creatinglandmarks on said generic crown further comprises projecting saidlandmarks onto a crown surface.
 12. The computer-implemented methodaccording to claim 1, wherein generating at least one patient toothmodel comprises: generating a patient crown tooth model without a rootcomponent; detecting of crown geometry from said patient crown toothmodel; and automatically creating landmarks on said patient crown toothmodel.
 13. The computer-implemented method according to claim 1, whereinmorphing said at least one patient tooth model with said at least onegeneric tooth model comprises: generating a morphing function;calculating a patient root component from said morphing function; andstitching a corresponding patient crown component to said patient rootcomponent.
 14. The computer-implemented method according to claim 13,wherein stitching a corresponding patient crown component to saidpatient root component comprises stitching said patient crown componentfor a particular tooth with said patient root component corresponding tosaid particular tooth.
 15. The computer-implemented method according toclaim 14, wherein stitching said patient crown component for aparticular tooth with said patient root component corresponding to saidparticular tooth is conducted for each tooth of a patient.
 16. Thecomputer-implemented method according to claim 13 wherein morphingfurther comprises smoothing the root-crown transition area.
 17. Thecomputer-implemented method according to claim 13, wherein morphingfurther comprises conducting interactive adjustment of said patient rootcomponent.
 18. The computer-implemented method according to claim 13,wherein calculating a morphing function comprises using a thin-platespline.
 19. The computer-implemented method according to claim 13,wherein calculating a patient root component comprises applying saidmorphing function on said generic tooth model.
 20. Thecomputer-implemented method according to claim 2, wherein segmenting ofsaid generic crown from said generic mesh further comprises generatingcrown and root mesh.
 21. The computer-implemented method according toclaim 20, wherein generating crown and root mesh comprises: constructinga three-dimensional spline curve through control point on a transitionarea between patient tooth crown and root; projecting saidthree-dimensional spline curve on a tooth mesh having triangle faces;calculating an intersection between a projected curve and edges of saidtriangle faces; and construct three new triangles using three originalvertices of an intersected triangle and two intersection points.
 22. Thecomputer-implemented method according to claim 21, wherein generatingcrown and root mesh further comprises: re-triangulating said intersectedtriangle and replace with said three new triangles; and removing allfaces below said projected curve to generate a new tooth mesh modelcomprising tooth crown.
 23. The computer-implemented method according toclaim 13, wherein morphing further comprises: utilizing crown landmarksto calculate the initial morphing function, which is used to determine amorphed central axis; repositioning a central axis of said generic toothmodel to be tangent to said morphed central axis; scaling saidrepositioned central axis of said generic tooth model to besubstantially equal to said morphed central axis in a z-direction; andcalculating a final morphing function through use of both the crownlandmarks and the root landmarks from said generic tooth model and saidpatient tooth model.
 24. The computer-implemented method according toclaim 23, wherein constructing said merged loop comprises resortingvertices of said merged loop.
 25. The computer-implemented methodaccording to claim 13, wherein stitching a corresponding patient crowncomponent to said patient root component comprises: projectingthree-dimensional loops onto an x-y plane; constructing a merged loop;re-triangulating a crown mesh and a root mesh; and merging said crownmesh with said root mesh.
 26. The computer-implemented method accordingto claim 13, wherein conducting interactive adjustment of said patientroot component comprises adjusting by at least one of length androtation.
 27. The computer-implemented method according to claim 1,wherein said computer-implemented method further comprises detailedadjustment modeling of said complete tooth model.
 28. Thecomputer-implemented method according to claim 27, wherein said detailedadjustment modeling comprises using actual root information associatedwith a particular tooth of the patient.
 29. The computer-implementedmethod according to claim 28, wherein said detailed adjustment modelingcomprises using actual X-ray imaging information associated with theparticular tooth of the patient.
 30. The computer-implemented methodaccording to claim 29, wherein said detailed adjustment modelingcomprises: projecting of said complete tooth model on a single planefrom a facial side to a lingual side; calculating a contour of saidcomplete tooth model; locating a corresponding patient tooth from saidX-ray information; calculating a contour of said corresponding patienttooth; determining a scale between said contour of said complete toothmodel and said contour of said corresponding patient tooth; and scalingsaid contour of said corresponding patient tooth to said contour of saidcomplete tooth model.
 31. The computer-implemented method according toclaim 30, wherein said detailed adjustment modeling comprises:generating landmarks on root domains of said complete tooth model's saidcontour and said corresponding patient tooth's said contour; andmorphing said root domains on said single plane.
 32. Thecomputer-implemented method according to claim 1, wherein saidcomputer-implemented method further comprises creating a root widget formanipulating tooth movement.
 33. The computer-implemented methodaccording to claim 1, wherein said computer-implemented method furthercomprises monitoring speed of movement of a tooth using root geometry.34. A computerized system for modeling of tooth root and crown of apatient to facilitate dental and/or orthodontic treatment, saidcomputerized modeling system comprising: a microprocessor comprising aplurality of algorithms; a memory device; and wherein said computerizedmodeling system is configured for generating: a three-dimensionaldigital crown model for a particular tooth of the patient; and athree-dimensional digital generic model comprising both a generic crowncomponent and a generic root component, said three-dimensional genericmodel configured for said particular tooth of said three-dimensionalcrown model; and wherein said computerized modeling system is configuredfor morphing said a three-dimensional crown model with saidthree-dimensional generic model to yield a complete three-dimensionalroot and crown tooth model for said particular tooth.
 35. Thecomputerized modeling system according to claim 34, wherein saidthree-dimensional generic model comprises a generic tooth templategenerated from scanning of a physical model for said particular tooth.36. The computerized modeling system according to claim 35, wherein saidcomputerized modeling system is configured for segmenting said genericcrown component from said generic root component, and for automatedcreation of landmarks on said generic crown component.
 37. Thecomputerized modeling system according to claim 36, wherein saidcomputerized modeling system is configured for automated creation oflandmarks on a crown component of said particular tooth.
 38. Thecomputerized modeling system according to claim 37, wherein saidcomputerized modeling system is configured for applying a morphingfunction on a generic root component to generate a patient rootcomponent and for stitching said crown component of said particulartooth to said generic root component to generate said completethree-dimensional root and crown tooth model.
 39. The computerizedmodeling system according to claim 38, wherein said computerizedmodeling system is configured for smoothing a crown-root transition areaof said complete three-dimensional root and crown tooth model.
 40. Thecomputerized modeling system according to claim 34, wherein saidcomputerized modeling system is configured for interactive rootadjustment.
 41. Digital representations of a plurality of teeth of apatient wherein the digital representation of the teeth are generated bythe following process: generating a plurality of actual patient toothmodels corresponding to each of the plurality of teeth, each of saidplurality of patient tooth models comprising corresponding crowncomponents; generating a plurality of generic tooth models correspondingto said plurality of patient tooth models, said plurality of generictooth model comprising both generic root and generic crown components;and morphing each of said plurality of patient tooth models with acorresponding one of said plurality of generic tooth models to provide acomplete tooth modeling for said plurality of teeth of the patient. 42.The digital representations according to claim 41, wherein generating aplurality of generic tooth models comprises generating a specific rootcomponent for a specific type of tooth.
 43. The digital representationsaccording to claim 42, wherein said process further comprises detailedadjustment modeling using actual root information associated with aparticular tooth of the patient.